Problems 101 to 200

Table 4.751: Solved using series method


#	ODE	Mathematica	Maple	Sympy

501	\[ {} 5 x y^{\prime \prime }+\left (30+3 x \right ) y^{\prime }+3 y = 0 \]	✓	✓	✓

502	\[ {} x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y = 0 \]	✓	✓	✗

503	\[ {} 2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

504	\[ {} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \]	✓	✓	✓

505	\[ {} 2 y-3 y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0 \]	✓	✓	✓

506	\[ {} x y^{\prime \prime }+y^{\prime }-x y = 0 \]	✓	✓	✓

507	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]	✓	✓	✓

508	\[ {} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y = 0 \]	✓	✓	✓

509	\[ {} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \]	✓	✓	✓

510	\[ {} x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y = 0 \]	✓	✓	✓

511	\[ {} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-4 y = 0 \]	✓	✓	✓

512	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \]	✓	✓	✓

513	\[ {} x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

1042	\[ {} y^{\prime } = y \]	✓	✓	✓

1043	\[ {} y^{\prime } = 4 y \]	✓	✓	✓

1044	\[ {} 2 y^{\prime }+3 y = 0 \]	✓	✓	✓

1045	\[ {} y^{\prime }+2 x y = 0 \]	✓	✓	✓

1046	\[ {} y^{\prime } = x^{2} y \]	✓	✓	✓

1047	\[ {} \left (x -2\right ) y^{\prime }+y = 0 \]	✓	✓	✓

1048	\[ {} \left (2 x -1\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

1049	\[ {} 2 y^{\prime } \left (1+x \right ) = y \]	✓	✓	✓

1050	\[ {} \left (x -1\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

1051	\[ {} 2 \left (x -1\right ) y^{\prime } = 3 y \]	✓	✓	✓

1052	\[ {} y^{\prime \prime } = y \]	✓	✓	✓

1053	\[ {} y^{\prime \prime } = 4 y \]	✓	✓	✓

1054	\[ {} y^{\prime \prime }+9 y = 0 \]	✓	✓	✓

1055	\[ {} y^{\prime \prime }+y = x \]	✓	✓	✗

1056	\[ {} x y^{\prime }+y = 0 \]	✓	✓	✗

1057	\[ {} 2 x y^{\prime } = y \]	✓	✓	✗

1058	\[ {} x^{2} y^{\prime }+y = 0 \]	✓	✗	✗

1059	\[ {} x^{3} y^{\prime } = 2 y \]	✓	✗	✗

1060	\[ {} y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

1061	\[ {} y^{\prime \prime }-4 y = 0 \]	✓	✓	✓

1062	\[ {} y^{\prime \prime }-2 y^{\prime }+y = 0 \]	✓	✓	✓

1063	\[ {} y^{\prime \prime }+y^{\prime }-2 y = 0 \]	✓	✓	✓

1064	\[ {} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \]	✓	✓	✗

1066	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]	✓	✓	✓

1067	\[ {} \left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]	✓	✓	✓

1068	\[ {} y+x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

1069	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]	✓	✓	✓

1070	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]	✓	✓	✓

1071	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]	✓	✓	✓

1072	\[ {} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]	✓	✓	✓

1073	\[ {} \left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0 \]	✓	✓	✓

1074	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]	✓	✓	✓

1075	\[ {} 3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \]	✓	✓	✓

1076	\[ {} 5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]	✓	✓	✓

1077	\[ {} y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]	✓	✓	✓

1078	\[ {} y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \]	✓	✓	✓

1079	\[ {} y^{\prime \prime }+x y = 0 \]	✓	✓	✓

1080	\[ {} y^{\prime \prime }+x^{2} y = 0 \]	✓	✓	✓

1081	\[ {} -2 y+2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

1082	\[ {} y^{\prime \prime }+x y^{\prime }-2 y = 0 \]	✓	✓	✓

1083	\[ {} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0 \]	✓	✓	✓

1084	\[ {} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0 \]	✓	✓	✓

1085	\[ {} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]	✓	✓	✓

1086	\[ {} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y \]	✓	✓	✓

1087	\[ {} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \]	✓	✓	✓

1088	\[ {} y^{\prime \prime }+\left (1+x \right ) y = 0 \]	✓	✓	✓

1089	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 x y = 0 \]	✓	✓	✓

1090	\[ {} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \]	✓	✓	✓

1091	\[ {} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0 \]	✓	✓	✓

1092	\[ {} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \]	✓	✓	✓

1093	\[ {} y^{\prime \prime }+y \,{\mathrm e}^{-x} = 0 \]	✓	✓	✓

1094	\[ {} y^{\prime \prime } \cos \left (x \right )+y = 0 \]	✓	✓	✓

1095	\[ {} x y^{\prime \prime }+y^{\prime } \sin \left (x \right )+x y = 0 \]	✓	✓	✓

1096	\[ {} y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0 \]	✓	✓	✓

1097	\[ {} y^{\prime \prime } = x y \]	✓	✓	✓

1361	\[ {} -y+y^{\prime \prime } = 0 \]	✓	✓	✓

1362	\[ {} y^{\prime \prime }-x y^{\prime }-y = 0 \]	✓	✓	✓

1363	\[ {} y^{\prime \prime }+k^{2} x^{2} y = 0 \]	✓	✓	✓

1364	\[ {} \left (1-x \right ) y^{\prime \prime }+y = 0 \]	✓	✓	✓

1365	\[ {} \left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]	✓	✓	✓

1366	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✓

1367	\[ {} 6 y-4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

1368	\[ {} \left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0 \]	✓	✓	✓

1369	\[ {} \left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \]	✓	✓	✓

1370	\[ {} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = 0 \]	✓	✓	✓

1371	\[ {} 2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \]	✓	✓	✓

1372	\[ {} y^{\prime \prime }-x y^{\prime }-y = 0 \]	✓	✓	✓

1373	\[ {} \left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]	✓	✓	✓

1374	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✓

1375	\[ {} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = 0 \]	✓	✓	✓

1376	\[ {} y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \]	✓	✓	✓

1377	\[ {} y^{\prime \prime }-x y^{\prime }-y = 0 \]	✓	✓	✓

1378	\[ {} \left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]	✓	✓	✓

1379	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✓

1380	\[ {} \left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✓

1381	\[ {} y^{\prime \prime }+x^{2} y = 0 \]	✓	✓	✓

1382	\[ {} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y = 0 \]	✓	✓	✓

1383	\[ {} y+x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

1384	\[ {} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 0 \]	✓	✓	✓

1385	\[ {} x^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )+3 y \ln \left (x \right ) = 0 \]	✓	✓	✓

1386	\[ {} y^{\prime \prime }+x^{2} y^{\prime }+\sin \left (x \right ) y = 0 \]	✓	✓	✓

1387	\[ {} y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \]	✓	✓	✓

1388	\[ {} y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \]	✓	✓	✓

1389	\[ {} \left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \]	✓	✓	✓

1390	\[ {} \left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \]	✓	✓	✓

1391	\[ {} \left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \]	✓	✓	✓

1392	\[ {} \left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \]	✓	✓	✓

4.7.2 Problems 101 to 200